一阶与二阶泛函微分方程的边值问题

Boundary Value Problems for First and Second Order Functional Differential Equations

本文考虑以下泛函微分方程的边值问题：“ｘ′（ｔ）＝ｆ（ｔ，ｘｔ）（０≤ｔ≤ｂ），ｘ０＝ｘｂ”及“ｘ”（ｔ）＝ｆ（ｔ，ｘｔ，ｘ′（ｔ））（０≤ｔ≤ｂ），ｘ０＝，ｘ（ｂ）＝Ｂ”。利用基于度理论的不动点定理，给出了上述边值问题有解的某些充分条件。

This paper considers the following boundary value problems for functional differential equations:'x'(t)=f(t,xt)(0≤t≤b),x0=xb'and'x'″(t)=f(t,xt,x′(t))(0≤t≤b),x0=,x(b)=B'.By using certain fixed point theorem based on the degree theory, some sufficient conditions for existence of solutions of the above problems are given.